Waveguides with Random Inhomogeneities and Brownian Motion In the Lobachevsky Plane

Gertsenshtein, M. E.; Vasil’ev, V. B.

doi:10.1137/1104038

Cited by 100 publications

(102 citation statements)

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“…This observation suggests a heuristic explanation as to why the DMPK equation can still be a good approximation when dL(s) is not distributed as in (16). By using the 'concentration of measure' property on the unitary group, see e.g.…”

Section: Of M(s) Is Haar Distributed In the Unitary Group And Indepenmentioning

confidence: 99%

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From the Anderson Model on a Strip to the DMPK Equation and Random Matrix Theory

Bachmann

Roeck

2010

J Stat Phys

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We study weakly disordered quantum wires whose width is large compared to the Fermi wavelength. It is conjectured that such wires display universal metallic behavior as long as their length is shorter than the localization length (which increases with the width). The random matrix theory that accounts for this behavior-the DMPK theory-rests on assumptions that are in general not satisfied by realistic microscopic models. Starting from the Anderson model on a strip, we show that a twofold scaling limit nevertheless allows to recover rigorously the fundaments of DMPK theory, thus opening a way to settle some conjectures on universal metallic behavior.

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Section: Of M(s) Is Haar Distributed In the Unitary Group And Indepenmentioning

confidence: 99%

“…The DMPK equation (24) for N = 1 was solved explicitly in [16]. It can be related to Brownian motion in the hyperbolic plane.…”

Section: Hyperbolic Brownian Motionmentioning

confidence: 99%

From the Anderson Model on a Strip to the DMPK Equation and Random Matrix Theory

Bachmann

Roeck

2010

J Stat Phys

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“…This relationship between reflection eigenvalues and Wigner-Smith delay times is useful because the efTects of absorption have received more attention in the literature than dynamic effects. In particular, the case of a single-mode disordered waveguide with absorption was solved äs early äs 1959, in the course of a radio-engineering problem [17]. The multi-mode case was solved more recently [18,19].…”

Section: Wigner-smith Delay Timementioning

confidence: 99%

Dynamics of localization in a waveguide

Beenakker

2001

Photonic Crystals and Light Localization in the 21st Century

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Abstract. This is a review of the dynamics of wave propagation through a disordered JV-mode waveguide in the localized regime. The basic quantities considered are the Wigner-Smith and single-mode delay times, plus the time-dependent power spectrum of a reflected pulse. The long-time dynamics is dominated by resonant transmission over length scales much larger than the localization length. The corresponding distribution of the Wigner-Smith delay times is the Laguerre ensemble of random-matrix theory. In the power spectrum the resonances show up äs a t~2 tail after Λ'' 2 scattering times. In the distribution of single-mode delay times the resonances introduce a dynamic coherent backscattering effect, that provides a way to distinguish localization from absorption.

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“…One such phenomenon that has drawn considerable attention over the years is Anderson localization, originally proposed in the framework of electron transport. Specifically, 50 years ago in the seminal work of Anderson [1,2], it was found that the classical (diffusive) picture was wrong, which assumed that the electrons perform random walks, yielding survival probability decays ∼ 1/ √ t and Ohmic conductance of G ∼ 1/L, where L is the system length (wire length). Due to wave interferences, a total halt of electronic propagation is found instead -leading to a converging non--zero return probability ∼ 1/l ∞ and to an exponential decay of the conductance G ∼ exp(−L/l ∞ ), where l ∞ is the so-called localization length.…”

Section: Introductionmentioning

confidence: 99%

Fidelity in Quasi-1D Systems as a Probe for Anderson Localization

et al. 2009

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We analyze the echo dynamics in quasi-one-dimensional random media to investigate how the transition from localization to delocalization is encoded in its temporal decay properties. Our analysis extends from the standard perturbative regime corresponding to small perturbations (with respect to the mean level spacing) in the echo dynamics, out to the Wigner decay regime. On the theoretical side, our results rely on a banded random matrix modeling, and show in the localized regime under small perturbations a novel decay of the fidelity (Loschmidt echo), differing from the typical Gaussian decay seen within both diffusive and chaotic systems. For larger perturbation strengths, typical Wigner exponential decays are observed. Scattering echo measurements are performed experimentally within a quasi-1D microwave cavity randomly populated with point-like scatterers. Agreements are observed between experiments, numerics, and theoretical predictions.

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Waveguides with Random Inhomogeneities and Brownian Motion In the Lobachevsky Plane

Cited by 100 publications

References 1 publication

From the Anderson Model on a Strip to the DMPK Equation and Random Matrix Theory

From the Anderson Model on a Strip to the DMPK Equation and Random Matrix Theory

Dynamics of localization in a waveguide

Fidelity in Quasi-1D Systems as a Probe for Anderson Localization

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